Of the four "BRIC" emerging market giants—Brazil, Russia, India and China—India is the best-performing nation, up 22 percent so far this year.

But since becoming prime minister in May, Modi hasn't shared a specific plan or agenda on plans to fix India's growing list of challenges—which includes rampant inflation, corruption and slowing growth.

Read MoreIndia's 2014/2015 GDP growth seen up at 5.9%

Modi has promised change, but investors want guidance on how he plans to stimulate the Indian economy.

"Now comes Modi's moment to showcase what him and the Bharatiya Janata Party have in store for citizens," Sam Gupta, CIO at Grand Trunk Capital, an India-focused investment fund, told CNBC.

"India's budgets matter. And the first one, after a tumultuous election, a decisive political verdict, and a huge market rally, probably matters even more."-Aditya Narain, Citi analyst

"The prime minister has spoken openly of the need to take bitter financial decisions," explained Manu Bhagavan, professor of history at Hunter College. "What exactly this translates to remains to be seen."

With the Bombay Sensex trading near record levels, investors are putting a laser-like focus on the budget. The Sensex edged lower overnight Wednesday.

"India's budgets matter," said Citi analyst Aditya Narain in a note to investors. "And the first one, after a tumultuous election, a decisive political verdict, and a huge market rally, probably matters even more. That this budget comes with significantly raised economic and market expectations, at a still-trying time for the economy (still-weak growth data, weak monsoons, and a pretty shaky external environment of late, and the recent oil spike) makes it a less predictable one."

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As for what Thursday's budget will include, market gurus have all sorts of forecasts, but Geoff Dennis, UBS head of Global Emerging Market Strategy, pointed to three items that investors are hoping to see.

"First and foremost, much enhanced privatization reform," said Dennis.

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The process of privatization, Dennis explained, will transfer assets from the public sector to the private sector, a strategy that should raise more revenue for the government. "That's revenue that can be used for growth purposes," Dennis said.

Privatization has been a popular policy globally since the 1980s, but in India, it has been a difficult process, especially during the reign of the previous administration under the Indian National Congress party.

The second agenda item, according to UBS, are policies and measures that promote infrastructure in India.

Infrastructure projects get stalled and held back in India on a regular basis, resulting in poorly made roads, heavy traffic and overcrowded railways. While several domestic and foreign corporations have tried to fix the problem, experts say bureaucratic red tape, corruption and a lack of decision-making at the state level result in projects' getting delayed.

The third item investors will be expecting the government to address on Thursday is one that's important everywhere: taxes. India has a complicated tax structure. Dennis expects Modi and the government to introduce a nationwide sales tax that will simplify tax reform.

Jonah Blank, senior political scientist at Rand Corp., said tax reform is one of the main items on the wish list of Indian businesses. "The goods and services tax, or GST, is the system by which taxes are levied and distributed by the (central government) and the states," he said. "It is a complex equation that needs simplification."

Whatever the budget holds, the policies and measures outlined by Modi's Bharatiya Janata Party on Thursday have a strong chance of being pushed forward, thanks to the new prime minister's broad election mandate.

"Prime Minister Modi has more freedom to make drastic economic reforms than any prime minister in decades," said Blank. "Whatever Modi proposes has a greater chance of passing Parliament."